In a neural network, can colors be used for neurons in place of floating points and would there be any benefit in doing so?
To answer your question, I'll just simplify it and assume you are representing the activation of a neuron (the value it produces) by an RGB value. So a tuple with 3 values ranging from 0 to 1.

It's important to remember that every single machine learning model could be computed by a human on pen and paper using just numbers. So keeping that in mind, this neural network would essentially just be a combination of multiplying tuples of size 3 in a certain order (ignoring activation functions). 

I will also assume that each RGB value has it's own unique set of incoming weights, like following:

this essentially amounts to just have 3 unique neurons. There's no difference:


All I did there was get rid of the circle. The calculations are no different. If you changed the calculation, say values are shared between the 3 RGB nodes, then you now just have 3 duplicate nodes. In all cases, you can just represent the equivalent calculation as a standard neural network.

However, in the same vein, in a convolutional neural network, if you create conv layers with an output of 3 channels, you can visualise their outputs as a colour image (assuming you are using an activation function that outputs numbers between 0 and 1), which can be cool to look at.